A corporation has a taxable income of $$6,570,000.$ At this income level, the federal income tax rate is $50\%,$ the

state tax rate is $20\%,$ and the local tax rate is $10\%.$ If each tax rate is applied to the total taxable income, the

resulting tax liability would be $80\%$ of taxable income. However, it is customary to deduct taxes paid to one

agency before computing taxes for the other agencies. Assume that the federal taxes are based on the income

that remains after the state and local taxes are deducted, and that state and local taxes are computed in a

similar manner. What is the tax liability of the corporation $($as a percentage of taxable income$)$ if these

deductions are taken into consideration? Construct a mathematical model. Use Gauss$-$Jordan elimination to

solve the model.

The tax liability of the corporation is $\%$ of the taxable income.

$($Round to the nearest hundredth as needed.$)$